Numerical analysis of a pile–slab-supported railway embankment

This paper presents a numerical analysis of a well-monitored pile–slab-supported embankment for the Beijing–Tianjin high-speed railway in China. Cement–fly ash–gravel piles were used in this project. A coupled two-dimensional mechanical and hydraulic numerical model was used for this analysis and the results are compared with the field measurements including settlement, load distribution between soil and pile, and excess pore pressure. The numerical model calculated the settlement profile close to that measured in the field. The proportion of the load carried by the soil was small thus significantly reducing the settlement. The stress transfer from the soil to the piles reduced the excess pore pressure effectively. A parametric study was conducted to investigate the influence of three key factors on the performance of the embankment. The parametric study indicated that the existence of a cushion reduced the shear force in the slab. The increase in slab thickness and pile stiffness increased the shear force and bending moment in the slab. An increase in pile stiffness reduced the settlement and lateral displacement of the embankment.     

Effect of the soil–pile–structure interaction in seismic analysis: case of liquefiable soils

The design of earthquake-resistant structures depends greatly on the soil–foundation–structure interaction. This interaction is more complex in the presence of liquefiable soils. Pile and rigid inclusion systems represent a useful practice to support structures in the presence of liquefiable soils in seismic zones. Both systems increase the bearing capacity of soil and allow reducing the settlements in the structure. Numerical models with a 3-storey reinforced concrete frame founded on inclusions systems (soil–inclusion–platform–structure) and pile systems (soil–pile–structure) were analyzed. Finite difference numerical models were developed using Flac 3D. Two different soil profiles were considered. A simple constitutive model for liquefaction analysis that relates the volumetric strain increment to the cyclic shear strain amplitude was utilized to represent the behavior of the sand, and the linear elastic perfectly plastic constitutive model with a Mohr–Coulomb failure criterion was used to represent the behavior of the earth platform. Two earthquakes were used to study the influence of the different frequency of excitation in the systems. The results were presented in terms of maximum shear forces distribution in the superstructure and spectrum response of each system. The efforts and displacements in the rigid elements (piles or rigid inclusions) were compared for the different systems. The bending and buckling failure modes of the pile were examined. The results show that the pile system, the soil profile and the frequency of excitation have a great influence on the magnitude and location of efforts and displacements in the rigid elements.

     

Explicit extension of the p–y method to pile groups in sandy soils

The method of “p–y” curves has been extensively used, in conjunction with simplified numerical methods, for the design and response evaluation of single piles. However, a straightforward application of the method to assess the response of pile groups is questionable when the group effect is disregarded. For this reason, the notion of p-multipliers has been therefore introduced to modify the “p–y” curves and account for pile group effect. The values proposed for p-multipliers result from pile group tests and are limited to the commonly applied spacing of 3.0 D and layout less than 3 × 3, restricting the applicability of the method to specific cases. With the aim of extending the applicability of the “p–y” method to pile groups, the authors have already proposed a methodology for estimating the “p _G–y _G” curves of soil resistance around a pile in a group for clayey soils. A complementary research allowing for the estimation of the “p _G–y _G” curves for sandy soils is presented in this paper. The well-known curves of soil resistance around the single pile in sandy soils are appropriately transformed to allow for the interaction effect between the piles in a group. Comparative examples validate the applicability and the effectiveness of the proposed method. In addition, the method can be straightforwardly extended to account for varying soil resistance, according to the particular location of a pile in a group. It can therefore be used in a most accurate manner in estimating the distribution of forces and bending moments along the characteristic piles of a group and therefore to design a pile foundation more accurately.     

Explicit extension of the p–y method to pile groups in cohesive soils

Although simplified numerical methods are reliable for evaluating the response of a single pile under horizontal load, their application is questionable for assessing the response of pile groups. The notion of “p–y” curves has been considered with the aim of establishing a transformation relationship able to provide the “p_G–y_G” curves of soil resistance around a pile in a group from the well-known curves of soil resistance around the single pile.This transformation extends the applicability of the “p–y” method to pile groups, without the need for time consuming numerical computations, rendering the proposed method efficient and attractive. Comparative examples demonstrated the applicability and the effectiveness of the proposed method. In addition, the method can be straightforwardly extended to account for varying soil resistance, according to the particular location of a pile in a group. It can therefore be used to estimate accurately force and bending moment distributions along the characteristic piles of a group, which are required for the efficient design of foundations.     

The dilatant behaviour of sand–pile interface subjected to loading and stress relief

Property and behaviour of sand–pile interface are crucial to shaft resistance of piles. Dilation or contraction of the interface soil induces change in normal stress, which in turn influences the shear stress mobilised at the interface. Although previous studies have demonstrated this mechanism by laboratory tests and numerical simulations, the interface responses are not analysed systematically in terms of soil state (i.e. density and stress level). The objective of this study is to understand and quantify any increase in normal stress of different pile–soil interfaces when they are subjected to loading and stress relief. Distinct element modelling was carried out. Input parameters and modelling procedure were verified by experimental data from laboratory element tests. Parametric simulations of shearbox tests were conducted under the constant normal stiffness, constant normal load and constant volume boundary conditions. Key parameters including initial normal stress ( $ \sigma_{{{\text{n}}0}}^{\prime } $ ), initial void ratio (e ₀), normal stiffness constraining the interface and loading–unloading stress history were investigated. It is shown that mobilised stress ratio ( $ \tau /\sigma_{\text{n}}^{\prime } $ ) and normal stress increment ( $ \Updelta \sigma_{\text{n}}^{\prime } $ ) on a given interface are governed by $ \sigma_{{{\text{n}}0}}^{\prime } $ and e ₀. An increase in $ \sigma_{{{\text{n}}0}}^{\prime } $ from 100 to 400 kPa leads to a 30 % reduction in $ \Updelta \sigma_{\text{n}}^{\prime } $ . An increase in e ₀ from 0.18 to 0.30 reduces $ \Updelta \sigma_{\text{n}}^{\prime } $ by more than 90 %, and therefore, shaft resistance is much lower for piles in loose sands. A unique relationship between $ \Updelta \sigma_{\text{n}}^{\prime } $ and normal stiffness is established for different soil states. It can be applied to assess the shaft resistance of piles in soils with different densities and subjected to loading and stress relief. Fairly good agreement is obtained between the calculated shaft resistance based on the proposed relationship and the measured results in centrifuge model tests.     

The effect of cemented soil strength on the frictional capacity of precast concrete pile–cemented soil interface

Acta Geotechnica - The pre-bored grouted planted (PGP) pile is a composite pile consisting of a precast concrete pile and the cemented soil around the pile. Thus, the PGP pile shaft capacity is...     

A finite element–based approach for predictions of rigid pile group stiffness efficiency in clays

This paper presents a finite element parametric study of several variables that affect the stiffness efficiency of rigidly capped pile groups with a view to developing a solution for preliminary design purposes. Previous empirical solutions from linear elastic work had identified a significant dependence of stiffness efficiency on pile group size and group spacing, and in this study, the effect of the pile length-to-diameter ratio, the compressibility of a stiff bearing stratum beneath the pile group and the depth below ground level to the stiff bearing stratum are also considered. Pile groups in a soft clay/silt are modelled using PLAXIS 3D Foundation in conjunction with a soil model that captures the stress dependency of soil stiffness. The trends from the soft soil study have been formulated into a set of equations which can be used to predict the stiffness efficiency of pile groups. This new approach captures more variables than previous simpler empirical prediction methods and performs better when applied to a database of 29 published pile group case histories.     

Analysis of soil resistance on laterally loaded piles based on 3D soil–pile interaction

The load distribution and deflection of large diameter piles are investigated by lateral load transfer method (p–y curve). Special attention is given to the soil continuity and soil resistance using three-dimensional finite element analysis. A framework for determining a p–y curve is calculated based on the surrounding soil stress. The appropriate parametric studies needed for verifying the p–y characteristic are presented in this paper. Through comparisons with results of field load tests, the three-dimensional numerical methodology in the present study is in good agreement with the general trend observed by in situ measurements and thus, represents a realistic soil–pile interaction for laterally loaded piles in clay than that of existing p–y method. It can be said that a rigorous numerical analysis can overcome the limitations of existing p–y methods to some extent by considering the effect of realistic three-dimensional combination of pile–soil forces.     

Discussion on “An analytical approach for the prediction of single pile and pile group behaviour in clay”

In the paper of Sheil and McCabe (2016), the ‘t–z method’ was used to capture the nonlinear response of single pile and pile group. However, some key questions on the skin friction and end resistance were not clearly addressed in their paper. In the present paper, analyses of the load transfer functions of the skin friction and end resistance are discussed in detail.     

Influence of spatial variability of soil friction angle on sheet pile walls’ structural behaviour

The uncertainty in terms of soil characterisation is studied to assess its effect on the structural behaviour of extended structures as sheet pile walls. A finite element model is used. This integrates a numerical model of the soil–structure interaction together with a stochastic model that allows characterising the soil variability. The model serves in propagating the variability and the system parameter uncertainties. Discussion is mainly focused on two points: (1) testing the sensitivity of the structural behaviour of a sheet pile wall to different geotechnical parameters and (2) assessing the influence of spatial variability of soil properties on the structural behaviour by identifying the most sensitive geotechnical parameter and the most significant correlation length values. The findings showed that in assessing the sheet pile wall’s structural behaviour, there are spatial variability parameters that cannot be considered negligible. In this study, soil friction angle is found to be an important parameter.     

A p–y curve model for laterally loaded XCC pile in soft clay

Acta Geotechnica - This paper presents a p–y curve model for laterally loaded X-sectional cast-in-place concrete (XCC) piles, which are a type of non-circular cross-sectional pile, in soft...     

Design charts for elastic pile shortening in the equivalent top–down load–settlement curve from a bidirectional load test

With a rigid pile assumption, the equivalent top–down load–settlement curve constructed from the results of a bidirectional or bottom–up pile load test does not fully consider the total elastic shortening when all the load components from skin-friction and end-bearing are applied downward at the pile head. In effect, the equivalent curve constructed by the original method suggested from the Osterberg test showed a much stiffer curve compared to the top–down curve. Design charts are provided in this paper from the results of a parametric study on bored piles in order to approximately evaluate the λ-factor that is used to estimate the top–down pile shortening from the bottom–up shortening due to the skin-friction component of the load. It has been shown that the λ-factor varies with the distribution of the undrained shear strength profile, pile slenderness ratio, and mobilization of the skin-friction resistance. In addition, the pile shortening due to the end-bearing load component is added to the top settlements by treating the pile as an elastic column. A modified method for the construction of the equivalent top–down load–settlement curve is presented that considers the elastic pile shortening and validated with the measured top–down load–settlement curve from pile load tests.     

Numerical analyses of uplift behavior of pile foundation for transmission line structure in frozen soil regions北大核心CSCD

Pile foundation is one of the most commonly used and suitable foundations to support transmission line structure, especially in seasonally frozen soil regions and permafrost regions. Axial compression is the controlling condition in the design of foundations for such structures as bridges and buildings, while uplift and overturning will control the design of transmission line structure foundations. This paper presents an extensive overview of previous studies including experimental (e. g., laboratory model test and full-scale field load test), analytical/theoretical (e. g., limit equilibrium and limit analysis based on plasticity)and numerical(e. g., finite difference and finite element methods). The review indicates that study on the uplift behavior of pile foundation in frozen soil is relatively limited, particularly in the case of combined effect of axial uplift and lateral loading. Interaction between pile and frozen soil and mechanism of load transfer along the pile shaft and around the pile tip still remain unclear. Therefore, this paper implements finite difference analysis within FLAC3D to investigate the behavior of pile foundation in frozen silty clay and gravelly sand under axial uplift behavior and the effect of ground condition and lateral loading on the uplift behavior. Because of the axisymmetric condition of the problem studied, only half of the model is simulated. The chosen domain of the medium is discretized into a set of quadrilateral elements and the pile is discretized by the cylinder element. The interaction between the soil and pile is considered according to interface elements. Mohr-Coulomb criterion is adopted to model the soil behavior (perfectly elastic-plastic), while the pile is simply considered as a rigid body. The soil parameters such as Young’s modulus, cohesion and internal friction angle used for numerical analyses are determined by laboratory tests and estimated according to the empirical correlations with in-situ tests. The present numerical modeling is verified with the results from field loading tests on pile foundations in Qinghai-Tibet ±550 kV transmission line project. On this basis, parametric studies are carried out to uncover the behavior of pile in frozen soil. It is observed that pullout is the dominant failure mechanism of pile and the uplift load-displacement curve clearly exhibits an asymptote, consisting of initially linear elastic, nonlinear transition, and finally linear regions. These results are consistent with the observations in a few previous studies. In addition, larger uplift capacity of pile foundation in freezing period and gravelly sand is gained (about 20%). Lateral loading increases the deflection and therefore, decreases the uplift capacity of pile foundation. For the convenience of using the results obtained in practice, the values of uplift factor for pile foundation in silty clay and gravelly sand are provided. Finally, it should be noted that the method used, and the results obtained in the current work could be useful for engineers and designers, at least providing them some qualitative evidence for pile design in seasonally frozen soil regions and permafrost regions. This is important and necessary to ensure the safety of construction in such regions. Meanwhile, numerical analyses in the current work can be a benchmark example for subsequent research studies. © 2022 Science Press (China).     

Response of 1 × 2 pile group under eccentric lateral loading

A large scale model test of a 1 × 2 pile group was conducted in silts to investigate its behavior under eccentric lateral loading. The model pile group consisted of two well instrumented steel piles and was installed in a large soil tank with a close spacing of three-pile diameters on centers. The test results revealed that the eccentricity of lateral loads had limited effect on the overall performances of the 1 × 2 pile group, but significantly contributed to the unevenness of internal forces of the individual piles. The coupling effect between the lateral deflection and torque gave rise to the substantial increase in the torsional resistance of individual piles within the group, comparing to that of a torsionally loaded single pile. The contribution provided by the torsional resistances of individual piles in resisting the external torque continually decreased when the applied lateral load increased. In addition, a three-dimensional finite-element analysis for the pile group was performed and the simulated response was found to be in good agreement with the measured test results. Based on the same model, more cases with different loading conditions were further analyzed. It could be concluded from the analyses that the layout of individual piles within the group obviously affected the behavior of the 1 × 2 pile group under eccentric lateral loads.     

P–V–T equations of state of MgO and thermodynamics

A simplest equation within the framework of the Mie-Grüneisen–Einstein approach is considered. Pressure estimation values are presented that are derived by conventional arithmetic and algebraic calculations as a function of temperature and volume. The equation under consideration complies with the Mie-Grüneisen–Debye model at high temperature. Different versions of an equation of state (EoS) of MgO proposed by Speziale et al. (J Geophys Res 106B:515–528, 2001) as a pressure standard at high temperatures are subject to analyses. In the literature, at least four versions of Speziale et al. EoS of MgO are discussed; the discrepancy between them reaching a few GPa at T > 2,000 K and P > 100 GPa. Our analyses of these equations suggest that the volume dependence of the Debye temperature is accepted arbitrarily and does not agree with the definition of the Grüneisen parameter, γ = −(∂lnΘ/∂lnV) _T . Pressure as a function of temperature and volume in the Mie-Grüneisen–Einstein approach or the Gao pressure calculator can be used to estimate true pressure at compression x = V/V ₀ < 1 with the Speziale et al. EoS of MgO.     

Results of U–Pb LA–ICP–MS dating of detrital zircons from Ediacaran–Early Cambrian deposits of the eastern part of the Baltic monoclise

Here we present the results of U–Pb LA–ICP–MS dating of detrital zircons from the Ediacaran–Early Cambrian deposits of the eastern part of the Baltic monoclise (Leningrad Region). The obtained age spectra of the detrital zircons suggest that, in the Ediacaran–Early Cambrian, the main clastic material source to the northwest of the Russian Platform was the Baltic Shield. Then in the Early Cambrian along with the Baltic Shield provenance, a clastic source from the Timanian margin of Baltica (northeast in modern coordinates) contributed to the deposits. The obtained data either somewhat set limits of the Timanian orogen formation as older than the previously suggested Middle Cambrian (about 510 Ma), based on the “absence of a Proto–Uralian–Timanian provenance signal” in the Sablino Formation rocks in the south Ladoga, or suggest another rearrangement of detritus transportation paths at the end of Stage 3 (Atdabanian).     

The P–V–T equation of state of CaPtO3 post-perovskite

Orthorhombic post-perovskite CaPtO₃ is isostructural with post-perovskite MgSiO₃, a deep-Earth phase stable only above 100 GPa. Energy-dispersive X-ray diffraction data (to 9.4 GPa and 1,024 K) for CaPtO₃ have been combined with published isothermal and isobaric measurements to determine its P–V–T equation of state (EoS). A third-order Birch–Murnaghan EoS was used, with the volumetric thermal expansion coefficient (at atmospheric pressure) represented by α(T) = α₀ + α₁(T). The fitted parameters had values: isothermal incompressibility, $ K_{{T_{0} }} $  = 168.4(3) GPa; $ K_{{T_{0} }}^{\prime } $  = 4.48(3) (both at 298 K); $ \partial K_{{T_{0} }} /\partial T $  = ?0.032(3) GPa K^?1; α₀ = 2.32(2) × 10^?5 K^?1; α₁ = 5.7(4) × 10^?9 K^?2. The volumetric isothermal Anderson–Grüneisen parameter, δ _T , is 7.6(7) at 298 K. $ \partial K_{{T_{0} }} /\partial T $ for CaPtO₃ is similar to that recently reported for CaIrO₃, differing significantly from values found at high pressure for MgSiO₃ post-perovskite (?0.0085(11) to ?0.024 GPa K^?1). We also report axial P–V–T EoS of similar form, the first for any post-perovskite. Fitted to the cubes of the axes, these gave $ \partial K_{{aT_{0} }} /\partial T $  = ?0.038(4) GPa K^?1; $ \partial K_{{bT_{0} }} /\partial T $  = ?0.021(2) GPa K^?1; $ \partial K_{{cT_{0} }} /\partial T $  = ?0.026(5) GPa K^?1, with δ _T  = 8.9(9), 7.4(7) and 4.6(9) for a, b and c, respectively. Although $ K_{{T_{0} }} $ is lowest for the b-axis, its incompressibility is the least temperature dependent.     

Minerals of the Fe–Ni–Co–Cu–S System in Picrite Intrusions of the Southern Urals: Signatures of Liquation and Differentiation of the Sulfide Melt

Doklady Earth Sciences - New data on the minerals of the Fe–Ni–Co–Cu–S system in the differentiated intrusions of the Southern Urals are presented. Based on a detailed study...